{"id":1286,"date":"2025-09-30T14:26:07","date_gmt":"2025-09-30T20:26:07","guid":{"rendered":"https:\/\/portal.pronea.gt\/?p=1286"},"modified":"2025-09-30T14:27:46","modified_gmt":"2025-09-30T20:27:46","slug":"temporary-title-790-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2","status":"publish","type":"post","link":"https:\/\/portal.pronea.gt\/?p=1286","title":{"rendered":"Sistema con ecuaciones e inc\u00f3gnitas"},"content":{"rendered":"<div id=\"cmsmasters_row_\" class=\"cmsmasters_row cmsmasters_color_scheme_default cmsmasters_row_top_default cmsmasters_row_bot_default cmsmasters_row_boxed\">\n<div class=\"cmsmasters_row_outer_parent\">\n<div class=\"cmsmasters_row_outer\">\n<div class=\"cmsmasters_row_inner\">\n<div class=\"cmsmasters_row_margin\">\n<div id=\"cmsmasters_column_\" class=\"cmsmasters_column one_first\">\n<div class=\"cmsmasters_column_inner\"><div class=\"cmsmasters_text\" data-animation=\"fadeIn\">\n<p data-start=\"2079\" data-end=\"2360\">Los <strong data-start=\"2083\" data-end=\"2124\">sistemas de ecuaciones con inc\u00f3gnitas<\/strong> son una herramienta matem\u00e1tica que nos permite resolver problemas donde varias variables est\u00e1n relacionadas entre s\u00ed. Lejos de ser complicados, son una forma organizada de encontrar soluciones concretas a situaciones de la vida real.<\/p>\n<p data-start=\"2362\" data-end=\"2437\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f3a5.svg\" alt=\"\ud83c\udfa5\" \/> <strong data-start=\"2365\" data-end=\"2387\">Mira el video aqu\u00ed<\/strong><\/p>\n<iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/r6WvVf_lEeo?si=4KlvGVisIUpm2H51\" width=\"1120\" height=\"630\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe>\n<hr data-start=\"2439\" data-end=\"2442\" \/>\n<h2 data-start=\"2444\" data-end=\"2485\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4cd.svg\" alt=\"\ud83d\udccd\" \/> \u00bfQu\u00e9 es un sistema de ecuaciones?<\/h2>\n<p data-start=\"2486\" data-end=\"2715\">Un <strong data-start=\"2489\" data-end=\"2514\">sistema de ecuaciones<\/strong> es un conjunto de dos o m\u00e1s ecuaciones que se deben resolver al mismo tiempo, ya que comparten las mismas inc\u00f3gnitas.<br data-start=\"2632\" data-end=\"2635\" \/>La meta es encontrar los valores que satisfacen todas las ecuaciones a la vez.<\/p>\n<p data-start=\"2717\" data-end=\"2727\">Ejemplo:<\/p>\n<p><em><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">x+y=10\u00a0 \u00a0 \u00a0 <\/span><\/span><\/span><\/em><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">y\u00a0 \u00a0 \u00a0 <\/span><\/span><\/span><em><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">x\u2212y=2<\/span><\/span><\/span><\/em><\/p>\n<hr data-start=\"2779\" data-end=\"2782\" \/>\n<h2 data-start=\"2784\" data-end=\"2837\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f6e0.svg\" alt=\"\ud83d\udee0\ufe0f\" \/> M\u00e9todos para resolver sistemas de ecuaciones<\/h2>\n<ol>\n<li data-start=\"2841\" data-end=\"2924\"><strong data-start=\"2841\" data-end=\"2857\">Sustituci\u00f3n:<\/strong> resolver una inc\u00f3gnita en una ecuaci\u00f3n y sustituirla en la otra.<\/li>\n<li data-start=\"2928\" data-end=\"2989\"><strong data-start=\"2928\" data-end=\"2943\">Igualaci\u00f3n:<\/strong> igualar expresiones y resolver paso a paso.<\/li>\n<li data-start=\"2993\" data-end=\"3069\"><strong data-start=\"2993\" data-end=\"3021\">Reducci\u00f3n o eliminaci\u00f3n:<\/strong> simplificar el sistema combinando ecuaciones.<\/li>\n<li data-start=\"3073\" data-end=\"3172\"><strong data-start=\"3073\" data-end=\"3094\">M\u00e9todos gr\u00e1ficos:<\/strong> representar en el plano cartesiano y ubicar la soluci\u00f3n en la intersecci\u00f3n.<\/li>\n<\/ol>\n<hr data-start=\"3174\" data-end=\"3177\" \/>\n<h2 data-start=\"3179\" data-end=\"3215\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f30d.svg\" alt=\"\ud83c\udf0d\" \/> Aplicaciones en la vida real<\/h2>\n<ul>\n<li data-start=\"3218\" data-end=\"3264\"><strong data-start=\"3218\" data-end=\"3231\">Econom\u00eda:<\/strong> calcular ingresos y gastos. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4b0.svg\" alt=\"\ud83d\udcb0\" \/><\/li>\n<li data-start=\"3267\" data-end=\"3323\"><strong data-start=\"3267\" data-end=\"3282\">Ingenier\u00eda:<\/strong> an\u00e1lisis de estructuras y fuerzas. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f3d7.svg\" alt=\"\ud83c\udfd7\ufe0f\" \/><\/li>\n<li data-start=\"3326\" data-end=\"3379\"><strong data-start=\"3326\" data-end=\"3345\">Administraci\u00f3n:<\/strong> organizar recursos y costos. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4ca.svg\" alt=\"\ud83d\udcca\" \/><\/li>\n<li data-start=\"3382\" data-end=\"3463\"><strong data-start=\"3382\" data-end=\"3401\">Vida cotidiana:<\/strong> resolver problemas con precios, cantidades o distancias. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f6b6.svg\" alt=\"\ud83d\udeb6\" \/><\/li>\n<\/ul>\n<hr data-start=\"3465\" data-end=\"3468\" \/>\n<h2 data-start=\"3470\" data-end=\"3497\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f393.svg\" alt=\"\ud83c\udf93\" \/> Aprender con PRONEA<\/h2>\n<p data-start=\"3498\" data-end=\"3808\">El <strong data-start=\"3501\" data-end=\"3556\">Programa Nacional de Educaci\u00f3n Alternativa \u2013PRONEA\u2013<\/strong> del Ministerio de Educaci\u00f3n de Guatemala ofrece materiales accesibles y claros para que j\u00f3venes y adultos comprendan los <strong data-start=\"3678\" data-end=\"3719\">sistemas de ecuaciones con inc\u00f3gnitas<\/strong>, fortaleciendo sus competencias matem\u00e1ticas y su capacidad de resoluci\u00f3n de problemas.<\/p>\n<hr data-start=\"3810\" data-end=\"3813\" \/>\n<h2 data-start=\"3815\" data-end=\"3832\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/2705.svg\" alt=\"\u2705\" \/> Conclusi\u00f3n<\/h2>\n<p data-start=\"3833\" data-end=\"4037\">Los <strong data-start=\"3837\" data-end=\"3863\">sistemas de ecuaciones<\/strong> no son solo un tema escolar: son una herramienta poderosa para resolver problemas de la vida real.<br data-start=\"3962\" data-end=\"3965\" \/>Con pr\u00e1ctica y estrategias claras, cualquier persona puede dominarlos.<\/p>\n<p data-start=\"4039\" data-end=\"4133\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f449.svg\" alt=\"\ud83d\udc49\" \/> Con el <strong data-start=\"4049\" data-end=\"4059\">PRONEA<\/strong>, aprender matem\u00e1ticas significa abrir m\u00e1s oportunidades para tu futuro.<\/p>\n<\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":1288,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"image","meta":{"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"footnotes":""},"categories":[33,39],"tags":[],"class_list":["post-1286","post","type-post","status-publish","format-image","has-post-thumbnail","hentry","category-matematicas","category-recursos","post_format-post-format-image"],"_links":{"self":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/1286","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1286"}],"version-history":[{"count":3,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/1286\/revisions"}],"predecessor-version":[{"id":1290,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/1286\/revisions\/1290"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/media\/1288"}],"wp:attachment":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1286"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1286"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1286"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}